H2–D2 Exchange Activity and Electronic Structure of AgxPd1–x Alloy Catalysts Spanning Composition Space

Many computational studies of catalytic surface reaction kinetics have demonstrated the existence of linear scaling relationships between physical descriptors of catalysts and reaction barriers on their surfaces. In this work, the relationship between catalyst activity, electronic structure, and alloy composition was investigated experimentally using a AgxPd1–x Composition Spread Alloy Film (CSAF) and a multichannel reactor array that allows measurement of steady-state reaction kinetics at 100 alloy compositions simultaneously. Steady-state H2–D2 exchange kinetics were measured at atmospheric pressure on AgxPd1–x catalysts over a temperature range of 333–593 K and a range of inlet H2 and D2 partial pressures. X-ray photoelectron spectroscopy (XPS) was used to characterize the CSAF by determining the local surface compositions and the valence band electronic structure at each composition. The valence band photoemission spectra showed that the average energy of the valence band, ε̅v, shifts linearly with composition from −6.2 eV for pure Ag to −3.4 eV for pure Pd. At all reaction conditions, the H2–D2 exchange activity was found to be highest on pure Pd and gradually decreased as the alloy was diluted with Ag until no activity was observed for compositions with xPd < 0.58. Measured H2–D2 exchange rates across the CSAF were fit using the Dual Subsurface Hydrogen (2H′) mechanism to extract estimates for the activation energy barriers to dissociative adsorption, ΔEads‡, associative desorption, ΔEdes‡, and the surface-to-subsurface diffusion energy, ΔEss, as a function of alloy composition, xPd. The 2H′ mechanism predicts ΔEads‡ = 0–10 kJ/mol, ΔEdes‡ = 30–65 kJ/mol, and ΔEss = 20–30 kJ/mol for all alloy compositions with xPd ≥ 0.64, including for the pure Pd catalyst (i.e., xPd = 1). For these Pd-rich catalysts, ΔEdes‡ and ΔEss appeared to increase by ∼5 kJ/mol with decreasing xPd. However, due to the coupling of kinetic parameters in the 2H′ mechanism, we are unable to exclude the possibility that the kinetic parameters predicted when xPd ≥ 0.64 are identical to those predicted for pure Pd. This suggests that H2–D2 exchange occurs only on bulk-like Pd domains, presumably due to the strong interactions between H2 and Pd. In this case, the decrease in catalytic activity with decreasing xPd can be explained by a reduction in the availability of surface Pd at high Ag compositions.


Quantification of uncertainty for ∆𝑬 𝒂𝒅𝒔
‡ , ∆  ‡ , and In order to estimate the uncertainty for ∆  ‡ , ∆  ‡ , and Δ  at the global minimum for each alloy, the Hessian matrix returned by the solver was used to construct a 3D hyper-ellipsoid bounding the region of 95% confidence around the solution.This 3D hyper-ellipsoid exists in parameter space for ∆  ‡ , ∆  ‡ , and Δ  , given by   ,   , and   , respectively, with the optimal solution at the center of the hyper-ellipsoid where  2 is at its minimum.Figures S1a-c demonstrate how the uncertainty for the kinetic parameters was calculated for Ag0.1Pd0.9.The global minimum in Figures S1a-c is marked by the blue dot at ∆  ‡ = 0 kJ/mol, ∆  ‡ = 44.8kJ/mol, and Δ  = 26.4kJ/mol.Grayscale contour maps within parameter space show how ln( 2 ) increases with respect to two kinetic parameters at a time when fixing the third to its value at the global minimum.In other words, Figure S1a shows the behavior of ln( 2 ) with respect to   and   when Δ  = 26.4kJ/mol, Figure S1b shows the behavior of ln( 2 ) with respect to   and   when ∆  ‡ = 44.8kJ/mol, and Figure S1c shows the behavior of ln( 2 ) with respect to   and   when ∆  ‡ = 0 kJ/mol.The red ellipses in Figures S1a-c are 2D cross sections of the 3D hyper-ellipsoid bounding the 95% confidence region when the third parameter is fixed at the global minimum.The red dashed lines trace the constant contour level of ln( 2 ) obtained after performing a Taylor expansion from the global minimum to any point on the red ellipses.
Note that the Taylor expansions for Figures S1a-c all yield the same value of ln( 2 ) so the red dashed line in each plot traces the same constant contour level within which any combination of kinetic parameters will yield statistically equivalent solutions with 95% confidence.Since the shape of the contour is difficult to interpret straightforwardly, black lines framing the extrema of the contour level within parameter space were drawn to show where they intersect with the x-and y-axis.The 95% confidence region for each kinetic parameter was obtained by defining ranges for ∆  ‡ , ∆  ‡ , and Δ  that are large enough to include all of the values framed by the black lines.For example, while the 95% confidence region for ∆  ‡ is 0 → 0.7 kJ/mol in Figure S1a,  and c) were drawn to frame the extrema of the red dashed lines within parameter space to show where they intersect with the axes.The 95% confidence region for each kinetic parameter was obtained by defining ranges for ∆  ‡ , ∆  ‡ , and Δ  that were large enough to include all parameter values within the black lines.For example, while the 95% confidence region for ∆  ‡ is 0 → 0.7 kJ/mol in a), the region for ∆  ‡ is 0 → 12.5 kJ/mol in b), and therefore, ∆  ‡ = 0 → 12.5 kJ/mol was chosen since it includes a larger range and is thus more conservative in defining the 95% confidence region.From a), b), and c), the 95% confidence regions for Ag0.1Pd0.9 are given by ∆  ‡ = 0 → 12.5 kJ/mol, ∆  ‡ = 29.7 → 57.6 kJ/mol, and Δ  = 20.1 → 26.8 kJ/mol.These ranges are shown by the error bars for Ag0.1Pd0.9 in Figure 7.
the region for ∆  ‡ is 0 → 12.5 kJ/mol in Figure S1b, and therefore, the larger range was chosen to make the estimate more conservative.Thus, from Figures S1a-c, the 95% confidence regions for the kinetic parameters for Ag0.1Pd0.9 are ∆  ‡ = 0 → 12.5 kJ/mol, ∆  ‡ = 29.7 → 57.6 kJ/mol, and Δ  = 20.1 → 26.8 kJ/mol.These ranges are shown by the error bars for Ag0.1Pd0.9 in Figure 7.The procedure above was used to estimate the uncertainties for the kinetic parameters predicted at all alloy compositions.

Determining outliers for fitted kinetic parameters based on 𝝌 𝟐
Due to inherent noise present in the data, the quality of the fit achieved at each set of optimized kinetic parameters, described by  2 , varied for each alloy composition.Figure S2a shows  2 versus   , and even though there is no obvious trend with respect to Pd content,  2 spans an order of magnitude across composition space.While it is clear from the optimization algorithm that solutions with high values of  2 have worse fits to the data, it can be difficult to determine the usefulness of the kinetic parameters predicted for each alloy composition without visualizing how the model-predicted values of HD production compare to experimental measurements.Figures S2b-d show the flow rate of HD,   (mol/s), versus the reaction temperature,  (K), under reaction conditions where  2  =  2  = 230 Torr for three alloy compositions (circled in red in Figure S2a), each with a progressively higher value of  2 .The alloy composition and value of  2 associated with the global minimum are printed on each graph.
The black data points in Figures S2b-d are the experimental values of   measured at the outlet of the microreactor channels and the red curves show the optimal fits using ∆  ‡ , ∆  ‡ , and Δ  in the equation for   given by the 2H' mechanism for H2-D2 exchange.When  2 is low, as for Ag0.1Pd0.9 in Figure S2b, a good fit to the data is achieved, however, as  2 increases, the quality of the fit diminishes.For example, when  2 = 43 in Figure S2c, some discrepancies between the experimental and model-predicted   are observed in the middle of the temperature range.Ultimately, when  2 increases to 113 in Figure S2d, the model-predicted   fails to reproduce the experimental data, as it overfits the data at low  and diverges significantly from experimental measurements for  ≥ 400 K. Consequently, the kinetic parameters corresponding to these predictions must be omitted from subsequent analysis since they do not appropriately characterize the data set.The cutoff value of  2 was chosen to be 1.5 ×

2
(the blue dashed line in a)) based upon the point at which visual analysis of   versus  shows a failure to fit the data properly.
It is important to note at this point that the data at  2  =  2  = 230 shown in Figures S2bd are only a subset of the entire set of   measurements used for the fitting.There are 13 other combinations of  2  and  2  for which   versus  can be plotted using the optimal kinetic parameters and it is the total sum of squared errors from these 196 data points that was used to calculate the value of  2 shown in Figures S2b-d.The key takeaway is that the quality of the fit to   shown in Figures S2b-d is similar at other combinations of  2  and  2  across the entire data set.This highlights the fact that even though the solver was able to converge on a global minimum within parameter space, this does not inherently mean that the estimated values of ∆  ‡ , ∆  ‡ , and Δ  are useful for describing H2-D2 exchange.
Based upon visual analysis of the fits of   versus  at different values of  2 , it was determined that an appropriate cutoff value for  2 was 1.5 ×   2 , where   2 is the average value of  2 across all data points.The cutoff value of  2 = 72.1 is marked by the blue dashed line in Figure S2a.All values of  2 below the cutoff correspond to global minima where the estimated kinetic parameters provide useful estimates for   across all ,  2  , and  2  .On the other hand, the 7 alloys having values of  2 above the cutoff correspond to solutions where there is significant overfitting to   at low  (as in Figure S2d), leading to poor   predictions across most reaction temperatures and all inlet pressure combinations.These solutions are outliers since they do not properly characterize H2-D2 exchange on AgxPd1-x alloy catalysts.Consequently, the kinetic parameters corresponding to these improper fits were removed from Figure 7 and were not included in the analysis of ∆  ‡ , ∆  ‡ , and Δ  as a function of   and ̅  .
3. Kinetic parameters ∆  ‡ , ∆  ‡ , and   versus  ̅ The kinetic parameters for H2-D2 exchange predicted by the 2H' mechanism, ∆  ‡ , ∆  ‡ , and Δ  , are plotted as a function of the average energy of the valence band, ̅  , in Figure S3.increases to between 15-45 kJ/mol, the range for ∆  ‡ narrows to between 50-70 kJ/mol, and ∆  decreases to between 5-20 kJ/mol.The activity of AgxPd1-x catalysts for H2-D2 exchange is negligible when the average valence band energy is less than -4.6 eV.

Figure S1 .
Figure S1.Grayscale map and contour plot of ln( 2 ) within   ,   ,   parameter space plotted around the global minimum for Ag0.1Pd0.9marked by the blue dot at ∆  ‡ = 0 kJ/mol, ∆  ‡ = 44.8kJ/mol, and Δ  = 26.4kJ/mol.The grayscale contour maps show how ln( 2 ) increases with respect to two kinetic parameters at a time when fixing the third to its value at the global minimum, i.e., a) Δ  = 26.4kJ/mol, b) ∆  ‡ = 44.8kJ/mol, and c) ∆  ‡ = 0 kJ/mol.The Hessian matrix returned by the solver at the global minimum was used to construct a 3D hyper-ellipsoid bounding the region of 95% confidence around the solution.The red ellipses in a), b), and c) are the 2D cross sections of the hyper-ellipsoid at the fixed value of the third parameter.The red dashed lines trace the constant contour level of ln( 2 ) obtained by performing a Taylor expansion from the global minimum at   2 to any point on the 95% confidence ellipses.Black lines in a), b),and c) were drawn to frame the extrema of the red dashed lines within parameter space to show where they intersect with the axes.The 95% confidence region for each kinetic parameter was obtained by defining ranges for ∆  ‡ , ∆  ‡ ,

Figure
Figure S2.a)  2 obtained from the best fit kinetic parameters for the 2H' mechanism versus   for   ≥ 0.58.All data points above the blue dashed line were excluded from Figure 7 due to a poor fit, with  2 > 1.5 ×   2 , where   2 is the average value of  2 .The data points highlighted by the red circles are shown in b), c), and d) where the flow rate of HD,   (mol/s), is plotted versus the reaction temperature,  (K), when  2  =  2  = 230 Torr for Ag0.1Pd0.9,Ag0.26Pd0.74,and Ag0.01Pd0.99,respectively.The black points are the experimental values of   measured at the outlet of the microreactor channels and the red curves show the modelpredicted   using the optimal kinetic parameters.When  2 is low (i.e.,  2 = 13 in b)), a good fit to the data is achieved, however, as  2 increases (i.e.,  2 = 43 in c)), the quality of the fit diminishes until it ultimately fails to capture the correct trend when  2 becomes too high (i.e.,  2 = 113 in d)).The deterioration of the fit from b) to c) to d) shows progressive overfitting to low temperature data as  2 increases, making a bad overall prediction for   .Consequently, the kinetic parameters corresponding to these predictions must be omitted from subsequent analysis since they do not appropriately characterize the data set.The cutoff value of  2 was chosen to be 1.5 ×